On steering in the C*-algebraic framework

TL;DR

This paper analyzes bipartite quantum steering within a C*-algebraic framework, establishing conditions for model equivalence, identifying scenarios with model gaps, and discussing implications for post-quantum steering and foundational problems.

Contribution

It formalizes quantum assemblages in a C*-algebraic setting, providing criteria for model equivalence and exploring the gap between models in specific measurement scenarios.

Findings

Equivalence of quantum commuting and tensor models under certain conditions

Existence of a model gap in scenarios with two measurement settings and more than two outcomes

No-go results for post-quantum steering in the bipartite paradigm

Abstract

We discuss a scenario of bipartite steering with local subsystems of the parties modeled by certain operator algebras. In particular, we formalize the notion of quantum assemblages in a commuting observables paradigm and focus on equivalent descriptions of such objects providing a systematic analysis of previously scattered approaches. We provide necessary and sufficient conditions for the equivalence of quantum commuting and tensor models that is stable under extensions of the trusted subsystem by arbitrary finite-dimensional ancillae. As a result, we show that the gap between two models of bipartite steering can be observed in an arbitrary scenario with two measurement settings ($m = 2$) and more than two outcomes ($k > 2$). Finally, we provide no-go results concerning the possibility of post-quantum steering in this most general bipartite paradigm and discuss related corollaries regarding free probability and operator system approach as well as a link to Tsirelson's problem.